# Automata theory in nominal sets

arXiv: https://arxiv.org/abs/1402.0897 · HTML: https://mlsanity.com/paper/1402.0897/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2014.

## Built on by (most cited first, 5 of 5)

- [Nominal Topology for Data Languages](https://mlsanity.com/paper/2304.13337/) (2023)
- [Bi-reachability in Petri nets with data](https://mlsanity.com/paper/2405.16176/) (2024)
- [Extracting Robust Register Automata from Neural Networks over Data Sequences](https://mlsanity.com/paper/2511.19100/) (2025)
- [Solvability of orbit-finite systems of linear equations](https://mlsanity.com/paper/2201.09060/) (2022)
- [Learning Canonical Register Automata over Ordered Data Domains](https://mlsanity.com/paper/2608.18765/) (2026)

## Abstract (arXiv)

We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an automorphism group of the alphabet. In the process, we generalize nominal sets due to Gabbay and Pitts.